Off on a Tangent

Off on a Tangent

A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics

November 7, 2007	Vol. 6, No. 5
http://www.math.hope.edu/newsletter.html

Algebraic geometry colloquium this week

Title:		When Algebra Meets Geometry
Speaker:		Prof. Darren Stephenson
Time:		Thursday, November 8 at 4:00 p.m.
Place:		VZN 240

Abstract: The subject of algebraic geometry involves a careful study of the link between geometric objects (curves, surfaces, etc.) and algebraic objects (polynomials, rings, ideals, etc.). Students often first encounter algebraic geometry when they learn that an algebraic equation like y = x² can be associated with a geometric object, the parabola given by the graph of y = x²in the xy-plane. We will detail this basic algebra-geometry correspondence at a more advanced level, culminating with a theorem called "Hilbert's Nullenstellensatz." We will also discuss ways in which algebra might shed light on geometric problems, and vice versa. Most of this talk should be accessible to students at all mathematical levels.

Colloquium scheduled for next week

Title:		Euler's Solution of the Basel Problem
Speaker:		Prof. Mark Pearson
Time:		Thursday, November 15 at 4:00 p.m.
Place:		VZN 240

Abstract: The year 2007 marks the 300th anniversary of the birth of Leonhard Euler, whom many people consider the greatest mathematician of all time. In this talk I'll discuss Euler's ingenious solution to the Basel Problem (What is the sum 1 + 1/4 + 1/9 + 1/16 + ... ?) and how this interesting chapter in the history of mathematics led to the Riemann Hypothesis, one of the most important unsolved problems of modern mathematics. Most of this talk should be accessible to students at all mathematical levels.

Elvis goes to Beantown

Elvis (and Prof. Pennings) will be the keynote speakers during the annual "Research by Undergraduates in Mathematics Boston University Symposium" in Boston this Saturday, November 10. The event is a forum for area undergraduates to come together and share their research in a poster session, and will be attended by students from multiple Boston-area institutions, including Boston University, Harvard University and the Massachusetts Institute of Technology.

Elvis has received international acclaim in his ability to determine the optimal route in which to retrieve a ball out of a lake. This is something that challenges most calculus students, but seems to be second nature to Elvis. To read more about the research Elvis has done, visit http://www.maa.org/mathland/mathtrek_06_09_03.html.

Students take part in MATH Challenge

We had a great turnout in this past Saturday's Michigan Autumn Take-Home Challenge (MATH Challenge). Hope had 33 enthusiastic (mostly), awake (kind of), cheerful (definitely), students on 11 teams.

Those participating were: Ben Herrman, Ben Gorsky, Ashten Wallace, Katie Heneveld, Katie Johnson, Jared Wabeke, Jake Van Den Berg, Wenfei Xue, Emily Bauss, Eric Lunderberg, Jeff Glupker, Leif Nelson, Andy Fransk, Ben Bockstege, Parth Patel, Ryan Converse, Megan Pearson, Ryan Sheets, PJ Walter, Eric O'Brien, Maurice Ouma, Andrew Lee, Brandon Bacon, Zach Mitchell, Nick Stegeman, Nick Holst, Ben Barkel, Joe Brandonisio, Terra Fox, Josh Kinder, Chris Hall, Curtis Moran, and Sab Schwiebert. Congratulations to all that accepted the Challenge!

Students attend MUMC

Eleven Hope students recently attended the tenth annual Michigan Undergraduate Mathematics Conference (MUMC) on Saturday, October 27 at Michigan State University. Students attending from Hope were Bryan McMahon, James Daly, Kaleb Topp, Sarah Dix, Timothy Boman, Ashley Gruenberg, Brian McLellan, Kayla Lankheet, Ryan Johnson, Shirley Bradley, Zachary Mitchell. The students were joined by Professors Bekmetjev, Edwards, and Stephenson.

MUMC gives undergraduate students from around Michigan a chance to give presentations in many areas of mathematics, statistics or related disciplines. Hope had three student presentations. Tim Bowman, Ryan Johnson, and Bryan McMahon presented "Death and Dismemberment in a Petri Dish: Modeling a Three-Level Interaction Using Nonlinear Dynamics," James Daly talked about "Graph Pebbling and Parallel Computing," and Brian McLellan presented "A Better Way to Estimate Disease Prevalence."

Student Challenge: MAA's You Tube Contest

The Mathematics Association of America (MAA) is introducing its first-ever MathTube Contest. The contest, open to teams of up to three undergraduate students, calls for creative videos that show the entertaining side of mathematics in a style similar to that of other such videos found on the popular website YouTube.

"I want people to put tongue firmly in cheek and show us what they've got," said Vallin, MAA's Associate Director for Student Activities. One of Vallin's favorite math-related YouTube videos, the popular Finite Simple Group (of Order Two) video by The Klein Four Group (http://www.youtube.com/watch?v=UTby_e4-Rhg), serves as a great example of the kind of creativity the panel of MAA judges will be looking for. The Klein Four Group performed here at Hope two years ago. For more information about this contest visit http://www.maa.org/news/100307mathtube.html.

The Problem of the Fortnight

Sequences: A sequence of numbers {a_n} has a₁ = 7 as its first term, and every other term after the first is defined as follows:

- if a term a_n is even, then the next term is a_n/ 2
- if a term a_n is odd, then the next term is 3a_n + 1

What is the 1000th term in this sequence?

Write your solution (not just the answer!) on your favorite picture of Leonhard Euler and drop it by Dr. Pearson's office (VWF 212) by noon on Friday, November 16. Be sure to write your name, the name(s) of your professor(s), and your math class(es) on your solution (e.g. Even Steven, Profs. Odd and Odder, Math 232 and 295).

Problem Solvers of the Fortnight

The Previous POF: In last fortnight's problem we had the equation Ax³ + (2 - A)x² - x - 1 = 0, where A is a real number for which the equation has three real roots, not necessarily distinct. For certain values of A, there is a repeated root r and a distinct root s. Our task was to list all values of the triple (A, r, s). The answers for this are (-3,1,-1/3) and (1,-1,1).

We had three students that were up to that task and gave us complete and correct solutions. Those students are Josh Borgg, Eric Lundberg, and Zachary Mitchell.

Every morning in Africa a gazelle wakes up. It knows it must run faster than the fastest lion or it will be killed. Every morning a lion wakes up and it knows it must run faster than the slowest gazelle or it will starve. It doesn't matter if you are the lion or the gazelle, when the sun comes up, you better be running. ~ Herb Caen

Off on a Tangent